Make sure the MacBook is fully shut down and unplugged before you attempt to clean the screen. No expensive cleaning kits, no chemicals.

Without 'sudo fdsetup authrestart' the login screen that shows up because the drive is locked, won't mirror to an external display.To clean your MacBook screen, you ideally want two microfibre (or lint-free) cloths – one for wet cleaning, one dry – and some water. When i say 'get past the password screen' i mean is that file vault will store the decryption key in ram, reboot, and then it will give you your regular login screen, where you enter your password. Once file vault is on, a simple 1 pass erase of the entire disk is good Sudo fdsetup authrestart to get past the password screen If u need to reboot and enter a password and the screen won't mirror. If there is some way of using your tv set to enable filevault, do that first before wiping.

anyway make sure you only wipe your main partition. once you have the mac book air connected to another mac using target disk mode, you can wipe it. i think your only alternative is to connect the macbook air to another computer, over firewire, or thunderbolt, depending on the configuration of your computer, and hold down the T key on the mac book air to turn on target disk mode. If you wipe the disk once, 7 times, or 35 times, and its a SSD, i heard someone can take a microscope to the flash memory or use some high tech stuff to read the data if you erase the disk just a simple erase with file vault on your protected you can wipe it 35 times, and some CIA person could still read it. there just isn't a way to reliablly erase a SSD.

if you have a newer SSD based macbook Air. I rushed out and rebooted my mac book pro connected to my tv to see if i could see the option screen on my tv set over hdmi!! and i didn't!!

Macbook air wipe clean